unit dimensions basic maths type 1 type 1

7/28/2019 Unit Dimensions Basic Maths Type 1 Type 1

1/6

Index

1. Key Concepts2. Exercise I

3. Exercise II

4. Exercise III

5. Exercise IV

6. Answer Key

7. 34 Yrs. Que. from IIT-JEE

8. 10 Yrs. Que. from AIEEE

Subject : PHYSICS

Topic : UNITS & DIMENSIONS + BASIC MATHS

Students Name :______________________

Class :______________________

Roll No. :______________________

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Page2of6UNITDIMNSIONBASICMATHS

EXERCISE

Q.1 If force, acceleration and time are taken as fundamental quantities, then the dimensions of length will be:

(A) FT2 (B) F1 A2 T1 (C) FA2T (D) AT2

Q.2 The dimensions ML1 T2 can correspond to :

(A) moment of a force or torque (B) surface tension

(C) pressure (D) co-efficient of viscosity.(useful relation are

=

r x F , S = F/l , F = 6 r, where symbols have usual meaning)

Q.3 Which of the following can be a set of fundamental quantities(A) length, velocity, time (B) momentum, mass, velocity

(C) force, mass, velocity (D) momentum, time, frequency

Q.4 Kinetic energy (K) depends upon momentum (p) and mass (m) of a body as K pa mb

(A) a =1; b =1 (B) a =2; b = 1 (C) a =2; b=1 (D) a =1; b =2

Q.5 If area (A) velocity (v) and density () are base units, then the dimensional formula of force can be

represented as.(A) Av (B) Av2 (C) Av2 (D) A2v

Q.6 The pressure of 106 dyne/cm2 is equivalent to

(A) 105 N/m2 (B) 106 N/m2 (C) 107 N/m2 (D) 108 N/m2

Q.7 If 1 unit of mass = 4 kg; 1 unit of length =4

1m and 1 unit of time = 5 sec, then 1 Joule =x units of energy

in this system wherex =

(A) 100 units (B) 0.01 units (C) 200 units (D) 0.02 units

Q.8 In a certain system of units, 1 unit of time is 5 sec, 1 unit of mass is 20 kg and unit of length is 10 m. In thissystem, one unit of power will correspond to

(A) 16 watts (B)1

16watts (C) 25 watts (D) none of these

Q.9 In a book, the answer for a particular question is expressed as

b =

+

ma

k21

k

ma l

here m represents mass, a represents accelerations , l represents length. The unit of b should be

(A) m/s (B) m/s

2

(C) meter (D) / sec.Q.10 If the resultant of two forces of magnitudes P and Q acting at a point at an angle of 60 is 7 Q, then

P / Q is

(A) 1 (B) 3 / 2 (C) 2 (D) 4

Q.11 The resultant of two forces F1 and F2 is P. If F2 is reversed, then resultant is Q. Then the value of

(P2 + Q2) in terms of F1 and F2 is

(A) 2(F12 + F2

2) (B) F12 + F2

2 (C) (F1 + F2)2 (D) none of these


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Q.12 A man moves towards 3 m north then 4 m towards east and finally 5m towards 37 south of west. Hisdisplacement from origin is

(A) m25 (B) 0 m (C) 1 m (D) 12 m

Q.13 Three forces P, Q & R are acting at a point in the plane . The angle between P & Q and Q & R are 150

& 120 respectively, then for equilibrium, forces P, Q & R are in the ratio

(A) 1 : 2 : 3 (B) 1 : 2 : 3 (C) 3 : 2 : 1 (D) 3 : 2 : 1

Q.14 A man rows a boat with a speed of 18km/hr in northwest direction. The shoreline makes an angle of 15south of west. Obtain the component of the velocity of the boat along the shoreline.

(A) 9 km/hr (B) 183

2km/hr (C) 18 cos15km/hr (D) 18 cos75 km/hr

Q.15 A bird moves from point (1, 2, 3) to (4, 2, 3) . If the speed of the bird is 10 m/sec, then the velocity

vector o f the bird is :

(A) 5 k3j2i + (B) 5 k3j2i4 ++ (C) j8.0i6.0 + (D) j8i6 +

Q.16 The resultant of two forces, one double the other in magnitude is perpendicular to the smaller of the two

forces. The angle between the two forces is

(A) 150 (B) 90 (C) 60 (D) 120

Q.17 If the angle between the unit vectors a and b is 60, then |ba| is

(A) 0 (B) 1 (C) 2 (D) 4

Q.18 For a particle moving in a straight line, the position of the particle at time (t) is given byx = t3 6t2 + 3t + 7

what is the velocity of the particle when its acceleration is zero ?(A) 9 ms1 (B) 12 ms1 (C) 3 ms1 (D) 42 ms1

Q.19 Use the approximation (1 + x)n 1 + nx, | x |


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Page4of6UNITDIMNSIONBASICMATHSQ.24 The equation of state for a real gas at high temperature is given by P =

bV

nRT

)bV(VT

a2/1

+

where n, P, V & T are number of moles, pressure, volume & temperature respect ively & R is theuniversal gas constant . Find the dimensions of constant 'a' in the above equation.

Q.25 The distance moved by a particle in time t from centre of a ring under the influence of its gravity is given

by x = a sin

t where a &

are constants. If

is found to depend on the radius of the ring (r), its mass(m) and universal gravitational constant (G), find using dimensional analysis an expression for in termsof r, m and G.

Q.26 If the velocity of light c, Gravitational constant G & Plank's constant h be chosen as fundamental units,find the dimension of mass, length & time in the new system.

Q.27 A satellite is orbiting around a planet. Its orbital velocity (v0) is found to depend upon(a) Radius of orbit (R)(b) Mass of planet (M)(c) Universal gravitation constant (G)

Using dimensional analysis find an expression relating orbital velocity (v0) to the above physical quantities.

Q.28 Two vectors have magnitudes 3 unit and 4 unit respectively. What should be the angle between them ifthe magnitude of the resultant is (a) 1 unit, (b) 5 unit and (c) 7 unit.

Q.29 When two forces of magnitude P and Q are perpendicular to each other, their resultant is of magnitude

R. When they are at an angle of 180 to each other their resultant is of magnitude2

R. Find the

ratio of P and Q.

Q.30 A body acted upon by 3 given forces is under equilibrium.

(a) If 1F

= 10 Nt., 2F

= 6 Nt.

Find the values of 3F

& angle ().

(b) Express2F

in unit vector form.

Q.31 If the four forces as shown are in equilibrium

Express1F

&

2F

in unit vector form .

Q.32 A part icle is acted upon by the forces ,k7j5ibF,kbjci5F,k3jai2F321

+=+=+=

,kaj6icF4 +=

. Find the values of the constants a, b, c in order that the particle will be in equilibrium.


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Q.33 A plane body has perpendicular axes OX and OY marked on it and is acted on by following forces5P in the direction OY4P in the direction OX10P in the direction OA where A is the point (3a, 4a)15P in the direction AB where B is the point ( a, a)

Express each force in the unit vector form & calculate the magnitude & direction of sum of the vector ofthese forces.

Q.34 A particle moves along the space curve r

= (t2 + t) i + (3t 2)j + (2t3 4t2) k .(t in sec, r in m) Find attime t = 2 the (a) velocity, (b) acceleration, (c) speed or magnitude of velocity and (d) magnitude ofacceleration .

Q.35 A vectorA of length 10 units makes an angle of 60 with a vector

B of length 6 units. Find the magnitude

of the vector differenceA

B & the angle it makes with vector

A .

Q.36 At time t the position vector of a particle of mass m = 3kg is given byr t i t j t k = +6 3 cos . Find the

resultant forceF (t), magnitude of its acceleration when t =

2& speed when t = .

Q.37 Given that the position vector of a particle moving in x-y plane is given by r = ( ) ( ) t i t j2 4 4 + . Find

(a) Equation of trajectory of the particle(b) Time when it crosses x-axis and y-axis

Q.38 The velocity time graph of a body moving in a straight line is shown.Find its

(a) instantaneous velocity at t = 1.5 sec.(b) average acceleration from t = 1.5 sec. to t = 2.5 sec.(c) draw its acceleration time graph from t = 0 to t = 2.5 sec

Q.39 The curvilinear motion of a particle is defined by vx=50-16t and y=100-4t2, where v

xis in metres per

second, y is in metres and t is in seconds. It is also known that x=0 when t=0. Determine the velocity (v)and acceleration(a) when the position y=0 is reached.

Q.40 The force acting on a body moving in a straight line is given by F = (3t2 4t +1) Newton where t is in sec.If mass of the body is 1kg and initially it was at rest at origin. Find

(a) displacement between time t = 0 and t = 2 sec.(b) distance travelled between time t = 0 and t = 2 sec.


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ANSWER KEY

EXERCISE

Q.1 D Q.2 C Q.3 C Q.4 B

Q.5 B Q.6 A Q.7 A Q.8 A

Q.9 C Q.10 C Q.11 A Q.12 B

Q.13 D Q.14 A Q.15 D Q.16 D

Q.17 B Q.18 A Q.19 (a) 9.95, (b) 0.99, (c) 4.986

Q.20 0.14, 0.09 Q.21 L1, ML2T2 Q.22 ML7T2

Q.23 T =k

ma Q.24 ML5T2K1/2 Q.25 = K

Gm

r3

Q.26 [M] = [h1/2c1/2G1/2]; [L] = [h1/2 c3/2G1/2]; [T] = [h1/2 c5/2 G1/2]

Q.27 v0 = k

R

GMQ.28 (a) 180, (b) 90, (c) 0 Q.29 2 3

Q.30 (a) |F|3

= 8 N, q = 90 (b)

2F

= i6

Q.311

F

= ( 312 1) j & j)15312(i)3512(F2 +=

Q.32 a = 7, b = 3, c = 4

Q.33 ]2[tan,P20,jP9iP12,jP8iP6,iP4,jP5 1 + with the +ve x axis

Q.34 (a) 5i + 3j + 8k, (b) 2i + 16k, (c) 27 , (d) 652

Q.35 2 19 ;cos17

2 19

Q.36 18 3t j t k cos ; 3p; 3 44 +

Q.37 (a) y2 + 8y +12 = x ; (b) crosses x axis when t = 4 sec. , crosses y axis when t = + 2 sec.

Q.38 ( ) / , ( ) / a m s b m s1

3

3

2

2, (c)

Q.39 j40i30v =

, j8i16a =

Q.40 (a)3

2m , (b) t = 0, 1

unit dimensions basic maths type 1 type 1

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